The strike is likely to add further pressure on the Israeli government to find a way to end the incessant rocket attacks.
The rockets reportedly struck the Zikim base, which is located north of the Gaza strip.
While there was no information on the severity of the injuries to the soldiers, two helicopters and around 20 ambulances were at the scene shortly after the incident.
The toll is the worst from Palestinian rocket attacks in months, when two Israelis died in separate attacks earlier this year.
Last week, Prime Minister Ehud Olmert warned Israel would "without hesitation and without pity" launch counter strikes against militants who open fire from the Gaza strip.
Mr Olmert also ordered the army to draw up plans to curb the rocket fire, but held back from endorsing water and power cuts on Gaza's beleaguered population.
There's been increasing pressure on the Israeli PM to respond to the incessant rocket fire against southern Israel, after an attack was carried out outside a day care centre in the hard hit town of Sderot.
Militants in Gaza regularly fire rockets and mortar rounds at Israel and while most of their rounds fall in open spaces, some populated areas have often been hit.
"The cabinet decided to continue the intensive military operations against those involved in terror and rocket launching," Olmert's office said after a government meeting on the rocket attacks.
While the cabinet decided against punitive measures against the impoverished population of Gaza, it instructed the security services to develop a new operational plan.
Defence Minister Ehud Barak was quoted as telling ministers that until Israel has completed development of a sophisticated rocket interception system, "the only solution is deep ground operations in Gaza."
"The time may be approaching where it will necessary to launch a major ground operation to stop the rocket fire," he said in a speech to directors of Israel's main arms manufacturing firms.